HTTP site fails with 404 request, but an HTTPS request works fine

Question

I work for a software company. We have an internal-only webservice being used by tablets in a warehouse for one of our clients. It's running on IIS on Windows Server 2012R2. We did an update to their test environment today which broke the webservice for their live system too.

Upon investigation, I learned that all http requests to the server by anything other than localhost/127.0.0.1 are failing, including the ones to the IIS default page. The requests return a 404 error. Connecting via https does technically work, but with a failed certificate. I am not in a position, as an employee of the software company and not their managed service provider, to fiddle with the certificate bindings to make that work on the tablets inside their network. Besides the certificate, which is not configured for internal access anyways, the site bindings look fine.

The system was rebooted, with no effect. I checked their firewall, and turning it all the way off does not make a difference. I checked powershell using Test-NetConnection on the machine's IP using port 443 and port 80. Both tests succeeded. I checked the Windows Event Viewer logs and nothing showed. I checked the IIS logs and found nothing. I checked worker processes but saw nothing since it's not a timeout, it's an instant 404. I even checked procmon just to see if there's even an attempt to access the directory. I admit I don't know how to use it to see if the IIS process is getting hit with a request.

I'm fresh out of ideas. Even the default website fails and I can't figure out what's wrong or what could have changed. The default website's web.config has no clues either.

What other routes of investigation might I be missing or not aware of to figure out what might have gone wrong?